If we don't know the sign of a variable, we have to be very careful about manipulating inequalities.salma wrote:Hi,
Can you plz help me with this question:
Is X+Y>0
1)X^2 - Y^2>1
2)X/Y +1>0
The actual answer is that the 2 statements together are not sufficient!!!!
My answer was B: from statement 2 we can get X/Y > -1, then X>-Y, then X+Y>0. Why is it wrong???
Thanks
Your first step was fine:
x/y + 1 > 0 ===> x/y > -1
However, to do the next step what you're actually doing is multiplying both sides by "y". If y is negative, that will flip the inequality.
So, if y is positive, we get:
x > -y
x + y > 0
However, if y is negative, we get:
x < -y
x + y < 0
Therefore, statement (2) is insufficient.
Statement (1) can be simplified as:
(x+y)(x-y) > 1
so, both terms could be + or both could be -. Also insufficient.
Even after combining, x+y could be greater or less than 0, so not enough information: choose (E).
